Abstract
Local convex ellipticity of a parametric integrand F at a given point in space and given tangent plane direction is defined. Using this definition, the same type of local regularity is proved for F-minimizing currents near points whose tangent planes are directions at which F is convexly elliptic, as holds for currents minimizing a globally elliptic integrand. Various notions of ellipticity are discussed. Finally, some examples are given of physically interesting parametric integrands that are only locally elliptic, and a conjecture is made as to the overall structure of surfaces minimizing the integrals of such integrands.
This research was partially supported by an NSF grant
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© 1988 Springer-Verlag
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Taylor, J.E. (1988). Local ellipticity of F and regularity of F minimizing currents. In: Chern, Ss. (eds) Partial Differential Equations. Lecture Notes in Mathematics, vol 1306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082932
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DOI: https://doi.org/10.1007/BFb0082932
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